The Proton-Proton Reaction
At the end of the first morning an abundance of hydrogen was distributed unevenly in clouds of gas with empty spaces between them. Mutual gravitational attraction within the clouds made them collapse. The increasing pressure raised the temperature. At high temperatures hydrogen nuclei move very rapidly in random directions, leaving behind the electrons they need to form hydrogen atoms. In such a frenetic dance the nuclei frequently have close encounters with one another. They do not collide like billiard balls since the nuclei repel each other because of their positive electrical charge.
The encounters are more like those of daredevil drivers that head toward each other but swerve away at the last moment in opposite directions. This is a very dangerous game, and no one recommends it.
Occasionally two nuclei come together nearly head on. If the temperature is high enough and the nuclei are moving fast enough, they may overcome their mutual electrical repulsion and stick together. Electrical repulsion is a long-range force. The strong nuclear force has a short range and can only bind two nuclei together when they are very close.
The direct fusion of hydrogen nuclei to make helium is called a proton-proton reaction. This is because a hydrogen atom, stripped of its electron, is usually just a bare proton. The proton-proton reaction prevailed in the first stars. We will save a discussion of the other important fusion reaction until the third morning.
Neutrons and Hydrogen to Deuterium
Collisions of protons with neutrons made the earliest deuterium. This reaction prevailed in the first few minutes of the universe, at the beginning of the first morning. However, a different nuclear reaction made deuterium during the second morning. There are few free neutrons in the interior of stars. If there were any when the star formed, after 13 minutes half of them emitted an electron and a neutrino and turned themselves into protons. After 130 minutes only one in a thousand of the original neutrons remained. Free neutrons do not last long enough to combine frequently with protons.
In the interior of a star it is much more likely that two protons will collide with each other. If they do, one of them will emit a positron and a neutrino, in the process turning itself into a neutron. The proton and the neutron then combine into one nucleus, a nucleus of deuterium. The formation of each deuterium nucleus releases 0.067 micro-microwatt-seconds of kinetic energy. This energy, called the binding energy, is the energy of the strong nuclear force.
The deuterium nucleus, the positron, and the neutrino each carry away a share of the binding energy as kinetic energy. The shares are variable, depending on the circumstances of the collision. The share of energy makes the particles move faster than they were moving before the reaction. This increase in speed raises the temperature of the mixture of nuclear particles. The positron finds an electron and the two annihilate themselves, releasing 0.164 micro-microwatt-seconds of energy in the form of gamma rays. These gamma rays gradually fracture into many light rays and heat waves.
Hydrogen and Deuterium to Lightweight Helium
When deuterium collides with hydrogen it forms a lightweight helium nucleus and emits a photon. The photon carries away 0.88 micro-microwatt-seconds of binding energy. Lightweight helium has the requisite two protons but only one neutron.
Lightweight Helium to Ordinary Helium
After many lightweight helium nuclei form there is a chance that two of them will collide. The result is one helium nucleus of regular weight with two neutrons, and two hydrogen nuclei consisting of one proton each. This reaction releases 2.060 micro-microwatt-seconds of binding energy.
Summary of the Proton-Proton Reaction
In the overall process above there had to be two hydrogen-hydrogen collisions to make two deuterium nuclei. Then there had to be two deuterium-hydrogen collisions for every collision of one lightweight helium nucleus with another. Six hydrogen nuclei enter the series of reactions, and two are produced, along with one helium nucleus. The helium nucleus is the net result from combining four hydrogen nuclei. The amount of energy released must be doubled for all the collisions except the last collision, since the first amounts correspond to reactions that must occur twice for each of the last reactions. The sum of energies for the first reactions is 0.067 + 0.164 + 0.880 = 1.111 micro-microwatt-seconds. Double this plus the energy of the last reaction is 2.222 + 2.060 = 4.282 micro-microwatt-seconds of energy. An average light photon has 0.360 micro-micro-microwatt-seconds of energy. Therefore four hydrogen atoms, when made into one helium atom, provide enough energy for 4 282 000/0.360 = 11.9 million photons of light.
This shows the great energy production of nuclear reactions. Chemical combustion of carbon with oxygen produces much less light per reaction. One needs two oxygen atoms to burn one carbon atom. Burning only one carbon atom produces heat, not light. Several carbon atoms must burn to raise the temperature to incandescence and make one photon of visible light.
The encounters are more like those of daredevil drivers that head toward each other but swerve away at the last moment in opposite directions. This is a very dangerous game, and no one recommends it.
Occasionally two nuclei come together nearly head on. If the temperature is high enough and the nuclei are moving fast enough, they may overcome their mutual electrical repulsion and stick together. Electrical repulsion is a long-range force. The strong nuclear force has a short range and can only bind two nuclei together when they are very close.
The direct fusion of hydrogen nuclei to make helium is called a proton-proton reaction. This is because a hydrogen atom, stripped of its electron, is usually just a bare proton. The proton-proton reaction prevailed in the first stars. We will save a discussion of the other important fusion reaction until the third morning.
Neutrons and Hydrogen to Deuterium
Collisions of protons with neutrons made the earliest deuterium. This reaction prevailed in the first few minutes of the universe, at the beginning of the first morning. However, a different nuclear reaction made deuterium during the second morning. There are few free neutrons in the interior of stars. If there were any when the star formed, after 13 minutes half of them emitted an electron and a neutrino and turned themselves into protons. After 130 minutes only one in a thousand of the original neutrons remained. Free neutrons do not last long enough to combine frequently with protons.
In the interior of a star it is much more likely that two protons will collide with each other. If they do, one of them will emit a positron and a neutrino, in the process turning itself into a neutron. The proton and the neutron then combine into one nucleus, a nucleus of deuterium. The formation of each deuterium nucleus releases 0.067 micro-microwatt-seconds of kinetic energy. This energy, called the binding energy, is the energy of the strong nuclear force.
The deuterium nucleus, the positron, and the neutrino each carry away a share of the binding energy as kinetic energy. The shares are variable, depending on the circumstances of the collision. The share of energy makes the particles move faster than they were moving before the reaction. This increase in speed raises the temperature of the mixture of nuclear particles. The positron finds an electron and the two annihilate themselves, releasing 0.164 micro-microwatt-seconds of energy in the form of gamma rays. These gamma rays gradually fracture into many light rays and heat waves.
Hydrogen and Deuterium to Lightweight Helium
When deuterium collides with hydrogen it forms a lightweight helium nucleus and emits a photon. The photon carries away 0.88 micro-microwatt-seconds of binding energy. Lightweight helium has the requisite two protons but only one neutron.
Lightweight Helium to Ordinary Helium
After many lightweight helium nuclei form there is a chance that two of them will collide. The result is one helium nucleus of regular weight with two neutrons, and two hydrogen nuclei consisting of one proton each. This reaction releases 2.060 micro-microwatt-seconds of binding energy.
Summary of the Proton-Proton Reaction
In the overall process above there had to be two hydrogen-hydrogen collisions to make two deuterium nuclei. Then there had to be two deuterium-hydrogen collisions for every collision of one lightweight helium nucleus with another. Six hydrogen nuclei enter the series of reactions, and two are produced, along with one helium nucleus. The helium nucleus is the net result from combining four hydrogen nuclei. The amount of energy released must be doubled for all the collisions except the last collision, since the first amounts correspond to reactions that must occur twice for each of the last reactions. The sum of energies for the first reactions is 0.067 + 0.164 + 0.880 = 1.111 micro-microwatt-seconds. Double this plus the energy of the last reaction is 2.222 + 2.060 = 4.282 micro-microwatt-seconds of energy. An average light photon has 0.360 micro-micro-microwatt-seconds of energy. Therefore four hydrogen atoms, when made into one helium atom, provide enough energy for 4 282 000/0.360 = 11.9 million photons of light.
This shows the great energy production of nuclear reactions. Chemical combustion of carbon with oxygen produces much less light per reaction. One needs two oxygen atoms to burn one carbon atom. Burning only one carbon atom produces heat, not light. Several carbon atoms must burn to raise the temperature to incandescence and make one photon of visible light.
